How to get an empty tracked by a camera to move smoothly between keyframes
I am suggesting you 


Backup and Archive your work
remove the cyclic dependency which means removing the limit distance constraints.  This information is provided in the console window.


Alternative 01


place the empty on newly created path.  Thus the camera is on path1 and the empty is on path2.
remove the limit distance constraints, repeated for emphasis
Please know that that changing a path changes its distance and thus keyframes on a path start moving.  If you can possibly  lay out the whole path for the empty at once or nearly so please try and be aware of the situation.  You have many follow path constraints with ebbing flowing [influence] as scary as this seems.  Sometimes the separation allows less work.


Alternative 02


This may or may not be an advanced technique alternative to the path constraint.  There is a [copy location] constraint with [influence] which may allow a object to reside a certain point at a certain keyframe with certainty once the time and effort of setting up the arrangement of objects and keyframes is made.